Popups within Web maps and web apps are extremely customizable and can be great for creating reports...However there is no way to print or export their contents! This seems like a basic feature that was either over looked or purposefully left out. I don't think it's technically difficult to implement. The only workflow that looks feasible right now requires the use of ArcGIS Server.
The ideal solution(in my mind) would be to add a "print" function at the bottom of the popup that would print the contents with formatting intact)